Abstract

This thesis is about creating a number of projective reconstructions of objects, with input data a set of point correspondences measured in a pair of images. Through these points, the Fundamental Matrix is first determined and subsequently, the Essential Matrix through the former. In both cases, 4 different types of reconstructions are created (2 with linear DLT intersections and 2 with non-linear), with the main difference that the reconstructions arising from the Fundamental Matrix lack the internal (calibration) information of the cameras, hence are projectively distorted. In contrast, the reconstruction arising from the Essential Matrix is similar to the real object, since the pair of the projection camera matrices computed includes the interior orientation of the images. To this purpose, algorithms in MatLab have been developed which take as input the coordinates of the corresponding points in two images, calculate first the Fundamental Matrix and subsequently the Essential Matrix from the former. Then, a number of pairs of projective camera matrices are computed, using the Fundamental and Essential Matrices, whereby, in the photogrammetric sense, the projective camera matrices reflect the interior and relative orientations of the cameras. Next, an intersection is programmed using the linear and non linear method of the Direct Linear Triangulation (DLT). In this thesis, the fundamental theoretical background is presented as well as the analysis of the algorithms developed for this purpose. Finally, a presentation, analysis and testing of the application algorithms with simulated and real data is included.